X-ray and neutron diffraction are among the most important techniques for nondestructive evaluation of stress. Diffraction elastic constants are necessary to translate lattice strain into macrostress. A new theory allows the calculation of diffraction elastic constants for arbitrary symmetry both of crystallites and specimen. The theory makes use of the equivalent inclusion method as well as of the solution of the anisotropic inclusion problem, and it assumes that the crystallite shape can be considered as, on average, spherical. The formalism can be applied in a very transparent way to any kind of aggregate containing crystallites.